Journal of Research of the National Bureau of Standards
AbstractThe integration of the storage differential equation at present is usually done mostly by graphical or numerical procedures. All approach to the analytical integration of that equation is the subject of this paper. A new method of fitting the given background curves by mathematically tractable expressions is introduced. The storage-outflow discharge relation is expressed in t he form of a power function. A general differential equation for water storage y'+cPy2-cy-k=0 is derived, with c and k constants for the given reservoir, outflow shape and type of flow, and P being the inflow hydrograph. The analytical solutions of this equation for P=0, P= constant, and certain P= f (t) are given for the integrable cases (tables 1 to 3, eqs (12) to (29)). The application of the results obtained is discussed at the end of the paper.
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